Pith Number

pith:CY56MVXN

pith:2026:CY56MVXNNE2DTJINNRCZ6ZMT5S

not attested not anchored not stored refs resolved

Boundary Value Problems on $p$-Adic Analytic Manifolds

Patrick Erik Bradley

Frame bundles on p-adic analytic manifolds yield coordinate Laplacians that support elliptic operators and solvable Dirichlet problems beyond compact subdomains.

arxiv:2605.16590 v1 · 2026-05-15 · math.NT · math.AP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{CY56MVXNNE2DTJINNRCZ6ZMT5S}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

Novel coordinate Laplacians on p-adic analytic n-manifolds are constructed with the help of frame bundles; these are used to construct elliptic operators for which related Dirichlet problems are formulated and solved, generalising results on compact subdomains of p-adic n-space.

C2weakest assumption

The frame-bundle construction produces coordinate Laplacians that are elliptic and permit well-posed Dirichlet problems on general p-adic analytic manifolds (as opposed to only compact subdomains of p-adic n-space).

C3one line summary

Introduces novel coordinate Laplacians on p-adic analytic n-manifolds via frame bundles to construct elliptic operators and solve generalized Dirichlet problems.

References

30 extracted · 30 resolved · 0 Pith anchors

[1] P.E. Bradley. Heat equations and hearing the genus on p-adic Mum ford curves via auto- morphic forms. Moscow Mathematical Journal, 25(4) (2025), 447–478 2025

[2] P.E. Bradley. Boundary Value Problems for p-Adic Elliptic Parisi-Z´ u˜ niga Diffusion, Journal of Pseudo-Differential Operators and Applications, 17 (2026), 1. 28 2026

[3] P.E. Bradley. Chapter 1: Diffusion on p-adic Analytic Manifolds , in: Compact Ultrametric Analytic Manifolds and Applications in Number Theory , ongoing habilitation project, Karls- ruhe Institute of 2026

[4] P.E. Bradley. Schottky invariant diffusion on the transcendent p-adic upper half plane , Non- linear Anal. 263 (2026), 113947 2026

[5] P.E. Bradley and A. Moran Ledezma. Hearing the Serre invariant of a compact p-adic ana- lytic manifold (2025), arXiv:2511.20631 [math.NT] 2025

Formal links

1 machine-checked theorem link

Receipt and verification

First computed	2026-05-20T00:02:31.451430Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

163be656ed693439a50d6c459f6593ec9980e4e1ee5e095c5344b734f932798b

Aliases

arxiv: 2605.16590 · arxiv_version: 2605.16590v1 · doi: 10.48550/arxiv.2605.16590 · pith_short_12: CY56MVXNNE2D · pith_short_16: CY56MVXNNE2DTJIN · pith_short_8: CY56MVXN

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/CY56MVXNNE2DTJINNRCZ6ZMT5S \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 163be656ed693439a50d6c459f6593ec9980e4e1ee5e095c5344b734f932798b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "697620d95fd9aa736349763b2916f6d633988d026c33499a122e95190d7ba7b7",
    "cross_cats_sorted": [
      "math.AP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2026-05-15T19:49:02Z",
    "title_canon_sha256": "08bfc1a266468882b74a35d9299ee4d75cce5e57650a1c529b2769100dd4f10f"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.16590",
    "kind": "arxiv",
    "version": 1
  }
}